It depends on what, precisely, you mean by “control.” I don’t mean to get picky with terminology here, but enforcing law and exerting influence through alliances are pretty distinct affairs.

The received wisdom is that direct control is mostly linked to how good your transportation system is. This mostly boils down to infrastructure. If roads are good and fresh horses lined up so that long distances can be covered quickly, a territory can be fairly large. One of the reasons the Mongols were likely so successful is because their military was highly mobile.

The other way to do things is have conquered (or subordinate) nations pay tribute, but mostly govern themselves.

These two approaches usually are not mutually exclusive and the most notable pre-industrial empires usually used both. The crux of your question essentially boils down to the ability to quickly project power either through military or diplomatic means. This is usually tied to the horse or speed of ships in some cases.

Although it should not be taken to mean that great infrastructure caused empire necessarily. The “raw material” obviously had to be there in the first place: economic power, military might, etc. Infrastructure, in other words, would have been a tool for exerting control, not really the means of conquest in the first place. (There is, however, some overlap.)